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22   Index rows, cols, cols2;
33 cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
38 cols2 = cols = MatrixType::ColsAtCompileTime;
52 Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
55 VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
57 MatrixType m1(rows, cols), m3(rows, cols2);
58 CMatrixType m2(cols, cols2);
59 createRandomPIMatrixOfRank(rank, rows, cols, m1);
69 MatrixType u(rows,cols);
72 l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
73 = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
82 VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
90 m2 = CMatrixType::Random(cols,cols2);
92 m2 = CMatrixType::Random(cols,cols2);
94 m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
117 VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
138 Index cols = rows;
140 MatrixType m1(cols, rows);